Analysis and Optimization of a Single-item Production System with Lead Time under General Periodic Review Inventory Policy

In this paper, a single-product inventory system with a general periodic review policy is considered on a discrete time. The number of products in inventory is reviewed periodically with a positive integer time interval, and new products are ordered under base stock policy. The amounts of demand are mutually independent and identically distributed with a general distribution. There is an integer production lead time, which may not be a multiple of the order interval. Zhang and Zhang (2007) derived an expression for the fill-rate of the demand. In this paper, we derive an expression for the average inventory and backlogs theoretically. We also consider an optimization problem for determining the optimal amount of base stock to minimize the long-time average inventory holding and backlog costs. An algorithm for deriving the optimal value is developed by using reverse Laplace transforms. The number of base stock for minimizing the average cost is also compared with the one satisfying the required fill rate.